Complex Integral Residue Theorem

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The discussion revolves around a problem involving the Complex Integral Residue Theorem, where the original poster shares a PDF of their attempted solution. They express confusion about a missing factor of f'(z) in their solution. Another participant points out that the limit expression for calculating the residue should involve (t-z)*t*f'(t)/(f(t)-w), correcting the misunderstanding about the cancellation of f(t)-w. The original poster acknowledges the mistake, realizing that f(t) should not cancel as it would for a simple pole. This exchange highlights the importance of accurately applying the residue theorem in complex analysis.
Tangent87
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I have attached a pdf of my problem and attempted solution. I seem to be a factor of f'(z) out from the required solution, can anyone see where I've gone wrong?
 

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Yes, shouldn't the expression you are taking the limit of to get the residue be (t-z)*t*f'(t)/(f(t)-w)?
 
Ahh yeah crap, I was thinking f(t)-w would cancel as usual when taking a residue of a simple pole but it's f(t) not t. Cheers.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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